Frank Freyer

Biophysical mechanisms of multistability in resting-state cortical rhythms

The human alpha (8–12 Hz) rhythm is one of the most prominent, robust, and widely studied attributes of ongoing cortical activity. Contrary to the prevalent notion that it simply “waxes and wanes,” spontaneous alpha activity bursts erratically between two distinct modes of activity. We now establish a mechanism for this multistable phenomenon in resting-state cortical recordings by characterizing the complex dynamics of a biophysical model of macroscopic corticothalamic activity. This is achieved by studying the predicted activity of cortical and thalamic neuronal populations in this model as a function of its dynamic stability and the role of nonspecific synaptic noise. We hence find that fluctuating noisy inputs into thalamic neurons elicit spontaneous bursts between low- and high-amplitude alpha oscillations when the system is near a particular type of dynamical instability, namely a subcritical Hopf bifurcation. When the postsynaptic potentials associated with these noisy inputs are modulated by cortical feedback, the SD of power within each of these modes scale in proportion to their mean, showing remarkable concordance with empirical data. Our state-dependent corticothalamic model hence exhibits multistability and scale-invariant fluctuations—key features of resting-state cortical activity and indeed, of human perception, cognition, and behavior—thus providing a unified account of these apparently divergent phenomena.

Bistability and Non-Gaussian Fluctuations in Spontaneous Cortical Activity

The brain is widely assumed to be a paradigmatic example of a complex, self-organizing system. As such, it should exhibit the classic hallmarks of nonlinearity, multistability, and “nondiffusivity” (large coherent fluctuations). Surprisingly, at least at the very large scale of neocortical dynamics, there is little empirical evidence to support this, and hence most computational and methodological frameworks for healthy brain activity have proceeded very reasonably from a purely linear and diffusive perspective. By studying the temporal fluctuations of power in human resting-state electroencephalograms, we show that, although these simple properties may hold true at some temporal scales, there is strong evidence for bistability and nondiffusivity in key brain rhythms. Bistability is manifest as nonclassic bursting between high- and low-amplitude modes in the alpha rhythm. Nondiffusivity is expressed through the irregular appearance of high amplitude “extremal” events in beta rhythm power fluctuations. The statistical robustness of these observations was confirmed through comparison with Gaussian-rendered phase-randomized surrogate data. Although there is a good conceptual framework for understanding bistability in cortical dynamics, the implications of the extremal events challenge existing frameworks for understanding large-scale brain systems.

How Ongoing Neuronal Oscillations Account for Evoked fMRI Variability

Variability of evoked single-trial responses despite constant input or task is a feature of large-scale brain signals recorded by fMRI. Initial evidence signified relevance of fMRI signal variability for perception and behavior. Yet the underlying intrinsic neuronal sources have not been previously substantiated. Here, we address this issue using simultaneous EEG–fMRI and real-time classification of ongoing alpha-rhythm states triggering visual stimulation in human subjects. We investigated whether spontaneous neuronal oscillations—as reflected in the posterior alpha rhythm—account for variability of evoked fMRI responses. Based on previous work, we specifically hypothesized linear superposition of fMRI activity related to fluctuations of ongoing alpha rhythm and a visually evoked fMRI response. We observed that spontaneous alpha-rhythm power fluctuations largely explain evoked fMRI response variance in extrastriate, thalamic, and cerebellar areas. For extrastriate areas, we confirmed the linear superposition hypothesis. We hence linked evoked fMRI response variability to an intrinsic rhythms power fluctuations. These findings contribute to our conceptual understanding of how brain rhythms can account for trial-by-trial variability in stimulus processing.

A canonical model of multistability and scale-invariance in biological systems

Multistability and scale-invariant fluctuations occur in a wide variety of biological organisms from bacteria to humans as well as financial, chemical and complex physical systems. Multistability refers to noise driven switches between multiple weakly stable states. Scale-invariant fluctuations arise when there is an approximately constant ratio between the mean and standard deviation of a systems fluctuations. Both are an important property of human perception, movement, decision making and computation and they occur together in the human alpha rhythm, imparting it with complex dynamical behavior. Here, we elucidate their fundamental dynamical mechanisms in a canonical model of nonlinear bifurcations under stochastic fluctuations. We find that the co-occurrence of multistability and scale-invariant fluctuations mandates two important dynamical properties: Multistability arises in the presence of a subcritical Hopf bifurcation, which generates co-existing attractors, whilst the introduction of multiplicative (state-dependent) noise ensures that as the system jumps between these attractors, fluctuations remain in constant proportion to their mean and their temporal statistics become long-tailed. The simple algebraic construction of this model affords a systematic analysis of the contribution of stochastic and nonlinear processes to cortical rhythms, complementing a recently proposed biophysical model. Similar dynamics also occur in a kinetic model of gene regulation, suggesting universality across a broad class of biological phenomena.

Ultrahigh-frequency EEG during fMRI: Pushing the limits of imaging-artifact correction

Although solutions for imaging-artifact correction in simultaneous EEG-fMRI are improving, residual artifacts after correction still considerably affect the EEG spectrum in the ultrafast frequency band above 100 Hz. Yet this band contains subtle but valuable physiological signatures such as fast gamma oscillations or evoked high-frequency (600 Hz) bursts related to spiking of thalamocortical and cortical neurons. Here we introduce a simultaneous EEG-fMRI approach that integrates hard and software modifications for continuous acquisition of ultrafast EEG oscillations during fMRI. Our approach is based upon and extends the established method of averaged artifact subtraction (AAS). Particularly for recovery of ultrahigh-frequency EEG signatures, AAS requires invariantly sampled and constant imaging-artifact waveforms to achieve optimal imaging-artifact correction. Consequently, we adjusted our acquisition setup such that both physiological ultrahigh-frequency EEG and invariantly sampled imaging artifacts were captured. In addition, we extended the AAS algorithm to cope with other, non-sampling related sources of imaging-artifact variations such as subject movements. A cascaded principal component analysis finally removed remaining imaging-artifact residuals. We provide a detailed evaluation of averaged ultrahigh-frequency signals and unaveraged broadband EEG spectra up to 1 kHz. Evoked nanovolt-sized high-frequency bursts were successfully recovered during periods of MR data acquisition afflicted by imaging artifacts in the millivolt range. Compared to periods without imaging artifacts they exhibited the same mean amplitudes, latencies and waveforms and a signal-to-noise ratio of 72%. Furthermore we identified consistent dipole sources. In conclusion, ultrafast EEG oscillations can be continuously monitored during fMRI using the proposed approach.

State-dependent perceptual learning.

Learning constitutes a fundamental property of the human brain—yet an unresolved puzzle is the profound variability of the learning success between individuals. Here we highlight the relevance of individual ongoing brain states as sources of the learning variability in exposure-based somatosensory perceptual learning. Electroencephalogram recordings of ongoing rhythmic brain activity before and during learning revealed that prelearning parietal alpha oscillations as well as during-learning stimulus-induced contralateral central alpha changes are predictive for the learning outcome. These two distinct alpha rhythm sources predicted up to 64% of the observed learning variability, one source representing an idling state with posteroparietal focus and a potential link to the default mode network, the other representing the sensorimotor mu rhythm, whose desynchronization is indicative for the degree of engagement of sensorimotor neuronal populations during application of the learning stimuli. Unspecific effects due to global shifts of attention or vigilance do not explain our observations. Our study thus suggests a brain state-dependency of perceptual learning success in humans opening new avenues for supportive learning tools in the clinical and educational realms.

EEG Quality:The Image Acquisition Artefact

In this chapter, we focus on the artefacts that arise in the EEG during the fMRI acquisition process. Functional MRI using echo planar imaging (EPI) sequences involves the application of rapidly varying magnetic field gradients for spatial encoding of the MR signal and radiofrequency (RF) pulses for spin excitation (see the chapter “The Basics of Functional Magnetic Resonance Imaging”). Early in the implementation of EEG–fMRI, it was observed that the acquisition of an MR image results in complete obscuration of the physiological EEG (Ives et al. 1993; Allen et al. 2000). Electromagnetic induction in the circuit formed by the electrodes, leads, patient and amplifier exposed to a time-varying magnetic field causes an electromotive force. Artefacts induced in the EEG by the scanning process have a strong deterministic component, due to the preprogrammed nature of the RF and gradient switching sequence, and therefore artefact correction is generally considered a lesser problem than pulse-related artefacts (see the chapter “EEG Quality: Origin and Reduction of the EEG Cardiac-Related Artefact”). According to Faraday’s law of induction, the induced electromotive force is proportional to the time derivative of the magnetic flux (summation of the magnetic field perpendicular to the circuit plane over the area circuit), dΦ/dt, and can therefore reflect changes in the field (gradient switching, RF) or in the circuit geometry or position relative to the field due to body motion (Lemieux et al. 1997). Therefore, the combination of body motion with image acquisition artefacts can lead to random variations that represent a real challenge for artefact correction.